An analogue of Hardy's theorem for the Heisenberg group

Thangavelu, S. (2001) An analogue of Hardy's theorem for the Heisenberg group Colloquium Mathematicum, 87 (1). pp. 137-145. ISSN 0010-1354

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Official URL: http://journals.impan.gov.pl/cm/Inf/87-1-9.html

Related URL: http://dx.doi.org/10.4064/cm87-1-9

Abstract

We observe that the theorem of Hardy on Fourior transform pairs can be reformulated in terms of the heat kernel associated with the Laplacian on the Euclidean space. This leads to an interesting version of Hardy's theorem for the sublaplacian on the Heisenberg group. We also consider certain Rockland operators on the Heisenberg group and Schrödinger operators on Rn Related to them.

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